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To remove burrs from your pet, crush the burr with a pair of pliers and work oil into the tangle. The burrs should then brush out easily.
Source: Making Life Easier tip book
By sooz from Toronto, ON
Be extremely careful when removing any burrs around the animal's face, near the eyes and behind. I can't stress that enough! All open areas of any animal can have the burrs travel up or into the area it is around. I repeat, those things TRAVEL!
My poor baby Poo Bear had one get into his eye. I only got to him after the accident but the pain involved going into any area is extremely horrible. Of course the reason it's called a burr is because it will "burrow it's way in." I brought him to the Vet ASAP but it was already bad. You see, the burrs can "walk", so to speak." They get into an area that is soft and they just keep going in until they no longer can. It's a horrible thing to happen.
If you use oil, I highly recommend olive oil. It's not only good on the skin, it's also soothing. You should always have an aloe plant handy. If the animal can't reach it, rub a piece of it over the infected area and it will help a lot. I can't say enough about the wonders of God's precious aloe plant. I have always used it for burns and I have never had a scar, no matter how close I have come to getting blisters. It's awesome! I pray that this helps.
By eseaters 
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Here are questions related to Removing Burrs from Your Pet's Fur.
I found a neighbor's Yorkshire running loose and took him in. I found the owner, but he is out of town right now. This little puppy is covered with burrs and I don't know how to remove them. I tried a dog comb, but it hurt him. Any hints would be appreciated.
By tikko marie 06/09/2012
Oil works - vegetable, baby oil rub it on the hair - burrs slide out. I clean up the oil with a wet washcloth that I rinse in a bucket next to the dog. Caution: sometimes the dog will try and drink the water - won't hurt them, but it does cause some stomach upset. As a child I would get burrs in my hair - grandma used vegetable oil and it didn't hurt.